Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(321,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.321");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 9x^{2} - 8x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 321.1 | ||
Root | \(0.500000 - 2.73709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.321 |
Dual form | 322.2.c.b.321.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | − | 1.41421i | − | 0.816497i | −0.912871 | − | 0.408248i | \(-0.866140\pi\) | ||
0.912871 | − | 0.408248i | \(-0.133860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.74166 | −1.67332 | −0.836660 | − | 0.547723i | \(-0.815495\pi\) | ||||
−0.836660 | + | 0.547723i | \(0.815495\pi\) | |||||||
\(6\) | 1.41421i | 0.577350i | ||||||||
\(7\) | 2.64575i | 1.00000i | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.74166 | 1.18322 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | − | 1.41421i | − | 0.408248i | ||||||
\(13\) | 5.65685i | 1.56893i | 0.620174 | + | 0.784465i | \(0.287062\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | − | 2.64575i | − | 0.707107i | ||||||
\(15\) | 5.29150i | 1.36626i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.74166 | 0.907485 | 0.453743 | − | 0.891133i | \(-0.350089\pi\) | ||||
0.453743 | + | 0.891133i | \(0.350089\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −3.74166 | −0.836660 | ||||||||
\(21\) | 3.74166 | 0.816497 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | + | 2.64575i | 0.834058 | + | 0.551677i | ||||
\(24\) | 1.41421i | 0.288675i | ||||||||
\(25\) | 9.00000 | 1.80000 | ||||||||
\(26\) | − | 5.65685i | − | 1.10940i | ||||||
\(27\) | − | 5.65685i | − | 1.08866i | ||||||
\(28\) | 2.64575i | 0.500000i | ||||||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | − | 5.29150i | − | 0.966092i | ||||||
\(31\) | 1.41421i | 0.254000i | 0.991903 | + | 0.127000i | \(0.0405349\pi\) | ||||
−0.991903 | + | 0.127000i | \(0.959465\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.74166 | −0.641689 | ||||||||
\(35\) | − | 9.89949i | − | 1.67332i | ||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.5830i | 1.73984i | 0.493197 | + | 0.869918i | \(0.335828\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.00000 | 1.28103 | ||||||||
\(40\) | 3.74166 | 0.591608 | ||||||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | −3.74166 | −0.577350 | ||||||||
\(43\) | 5.29150i | 0.806947i | 0.914991 | + | 0.403473i | \(0.132197\pi\) | ||||
−0.914991 | + | 0.403473i | \(0.867803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.74166 | −0.557773 | ||||||||
\(46\) | −4.00000 | − | 2.64575i | −0.589768 | − | 0.390095i | ||||
\(47\) | 7.07107i | 1.03142i | 0.856763 | + | 0.515711i | \(0.172472\pi\) | ||||
−0.856763 | + | 0.515711i | \(0.827528\pi\) | |||||||
\(48\) | − | 1.41421i | − | 0.204124i | ||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | −9.00000 | −1.27279 | ||||||||
\(51\) | − | 5.29150i | − | 0.740959i | ||||||
\(52\) | 5.65685i | 0.784465i | ||||||||
\(53\) | − | 10.5830i | − | 1.45369i | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||
0.686803 | − | 0.726844i | \(-0.259014\pi\) | |||||||
\(54\) | 5.65685i | 0.769800i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 2.64575i | − | 0.353553i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.00000 | 1.05045 | ||||||||
\(59\) | 9.89949i | 1.28880i | 0.764687 | + | 0.644402i | \(0.222894\pi\) | ||||
−0.764687 | + | 0.644402i | \(0.777106\pi\) | |||||||
\(60\) | 5.29150i | 0.683130i | ||||||||
\(61\) | −3.74166 | −0.479070 | −0.239535 | − | 0.970888i | \(-0.576995\pi\) | ||||
−0.239535 | + | 0.970888i | \(0.576995\pi\) | |||||||
\(62\) | − | 1.41421i | − | 0.179605i | ||||||
\(63\) | 2.64575i | 0.333333i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | − | 21.1660i | − | 2.62532i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 3.74166 | 0.453743 | ||||||||
\(69\) | 3.74166 | − | 5.65685i | 0.450443 | − | 0.681005i | ||||
\(70\) | 9.89949i | 1.18322i | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | − | 11.3137i | − | 1.32417i | −0.749429 | − | 0.662085i | \(-0.769672\pi\) | ||
0.749429 | − | 0.662085i | \(-0.230328\pi\) | |||||||
\(74\) | − | 10.5830i | − | 1.23025i | ||||||
\(75\) | − | 12.7279i | − | 1.46969i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.00000 | −0.905822 | ||||||||
\(79\) | − | 10.5830i | − | 1.19068i | −0.803473 | − | 0.595341i | \(-0.797017\pi\) | ||
0.803473 | − | 0.595341i | \(-0.202983\pi\) | |||||||
\(80\) | −3.74166 | −0.418330 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | − | 5.65685i | − | 0.624695i | ||||||
\(83\) | 14.9666 | 1.64280 | 0.821401 | − | 0.570352i | \(-0.193193\pi\) | ||||
0.821401 | + | 0.570352i | \(0.193193\pi\) | |||||||
\(84\) | 3.74166 | 0.408248 | ||||||||
\(85\) | −14.0000 | −1.51851 | ||||||||
\(86\) | − | 5.29150i | − | 0.570597i | ||||||
\(87\) | 11.3137i | 1.21296i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.2250 | −1.18984 | −0.594922 | − | 0.803783i | \(-0.702817\pi\) | ||||
−0.594922 | + | 0.803783i | \(0.702817\pi\) | |||||||
\(90\) | 3.74166 | 0.394405 | ||||||||
\(91\) | −14.9666 | −1.56893 | ||||||||
\(92\) | 4.00000 | + | 2.64575i | 0.417029 | + | 0.275839i | ||||
\(93\) | 2.00000 | 0.207390 | ||||||||
\(94\) | − | 7.07107i | − | 0.729325i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.41421i | 0.144338i | ||||||||
\(97\) | −3.74166 | −0.379908 | −0.189954 | − | 0.981793i | \(-0.560834\pi\) | ||||
−0.189954 | + | 0.981793i | \(0.560834\pi\) | |||||||
\(98\) | 7.00000 | 0.707107 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.00000 | 0.900000 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 5.29150i | 0.523937i | ||||||||
\(103\) | 14.9666 | 1.47471 | 0.737353 | − | 0.675508i | \(-0.236075\pi\) | ||||
0.737353 | + | 0.675508i | \(0.236075\pi\) | |||||||
\(104\) | − | 5.65685i | − | 0.554700i | ||||||
\(105\) | −14.0000 | −1.36626 | ||||||||
\(106\) | 10.5830i | 1.02791i | ||||||||
\(107\) | 5.29150i | 0.511549i | 0.966736 | + | 0.255774i | \(0.0823304\pi\) | ||||
−0.966736 | + | 0.255774i | \(0.917670\pi\) | |||||||
\(108\) | − | 5.65685i | − | 0.544331i | ||||||
\(109\) | − | 10.5830i | − | 1.01367i | −0.862044 | − | 0.506834i | \(-0.830816\pi\) | ||
0.862044 | − | 0.506834i | \(-0.169184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.9666 | 1.42057 | ||||||||
\(112\) | 2.64575i | 0.250000i | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.9666 | − | 9.89949i | −1.39565 | − | 0.923133i | ||||
\(116\) | −8.00000 | −0.742781 | ||||||||
\(117\) | 5.65685i | 0.522976i | ||||||||
\(118\) | − | 9.89949i | − | 0.911322i | ||||||
\(119\) | 9.89949i | 0.907485i | ||||||||
\(120\) | − | 5.29150i | − | 0.483046i | ||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 3.74166 | 0.338754 | ||||||||
\(123\) | 8.00000 | 0.721336 | ||||||||
\(124\) | 1.41421i | 0.127000i | ||||||||
\(125\) | −14.9666 | −1.33866 | ||||||||
\(126\) | − | 2.64575i | − | 0.235702i | ||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.48331 | 0.658869 | ||||||||
\(130\) | 21.1660i | 1.85638i | ||||||||
\(131\) | 12.7279i | 1.11204i | 0.831168 | + | 0.556022i | \(0.187673\pi\) | ||||
−0.831168 | + | 0.556022i | \(0.812327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.1660i | 1.82168i | ||||||||
\(136\) | −3.74166 | −0.320844 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | −3.74166 | + | 5.65685i | −0.318511 | + | 0.481543i | ||||
\(139\) | 4.24264i | 0.359856i | 0.983680 | + | 0.179928i | \(0.0575865\pi\) | ||||
−0.983680 | + | 0.179928i | \(0.942414\pi\) | |||||||
\(140\) | − | 9.89949i | − | 0.836660i | ||||||
\(141\) | 10.0000 | 0.842152 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 29.9333 | 2.48582 | ||||||||
\(146\) | 11.3137i | 0.936329i | ||||||||
\(147\) | 9.89949i | 0.816497i | ||||||||
\(148\) | 10.5830i | 0.869918i | ||||||||
\(149\) | − | 10.5830i | − | 0.866994i | −0.901155 | − | 0.433497i | \(-0.857280\pi\) | ||
0.901155 | − | 0.433497i | \(-0.142720\pi\) | |||||||
\(150\) | 12.7279i | 1.03923i | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.74166 | 0.302495 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.29150i | − | 0.425024i | ||||||
\(156\) | 8.00000 | 0.640513 | ||||||||
\(157\) | −11.2250 | −0.895850 | −0.447925 | − | 0.894071i | \(-0.647837\pi\) | ||||
−0.447925 | + | 0.894071i | \(0.647837\pi\) | |||||||
\(158\) | 10.5830i | 0.841939i | ||||||||
\(159\) | −14.9666 | −1.18693 | ||||||||
\(160\) | 3.74166 | 0.295804 | ||||||||
\(161\) | −7.00000 | + | 10.5830i | −0.551677 | + | 0.834058i | ||||
\(162\) | 5.00000 | 0.392837 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 5.65685i | 0.441726i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.9666 | −1.16164 | ||||||||
\(167\) | − | 9.89949i | − | 0.766046i | −0.923739 | − | 0.383023i | \(-0.874883\pi\) | ||
0.923739 | − | 0.383023i | \(-0.125117\pi\) | |||||||
\(168\) | −3.74166 | −0.288675 | ||||||||
\(169\) | −19.0000 | −1.46154 | ||||||||
\(170\) | 14.0000 | 1.07375 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.29150i | 0.403473i | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | − | 11.3137i | − | 0.857690i | ||||||
\(175\) | 23.8118i | 1.80000i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.0000 | 1.05230 | ||||||||
\(178\) | 11.2250 | 0.841347 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | −3.74166 | −0.278887 | ||||||||
\(181\) | −11.2250 | −0.834346 | −0.417173 | − | 0.908827i | \(-0.636979\pi\) | ||||
−0.417173 | + | 0.908827i | \(0.636979\pi\) | |||||||
\(182\) | 14.9666 | 1.10940 | ||||||||
\(183\) | 5.29150i | 0.391159i | ||||||||
\(184\) | −4.00000 | − | 2.64575i | −0.294884 | − | 0.195047i | ||||
\(185\) | − | 39.5980i | − | 2.91130i | ||||||
\(186\) | −2.00000 | −0.146647 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.07107i | 0.515711i | ||||||||
\(189\) | 14.9666 | 1.08866 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.8745i | 1.14864i | 0.818631 | + | 0.574320i | \(0.194733\pi\) | ||||
−0.818631 | + | 0.574320i | \(0.805267\pi\) | |||||||
\(192\) | − | 1.41421i | − | 0.102062i | ||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 3.74166 | 0.268635 | ||||||||
\(195\) | −29.9333 | −2.14357 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −9.00000 | −0.636396 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 21.1660i | − | 1.48556i | ||||||
\(204\) | − | 5.29150i | − | 0.370479i | ||||||
\(205\) | − | 21.1660i | − | 1.47830i | ||||||
\(206\) | −14.9666 | −1.04277 | ||||||||
\(207\) | 4.00000 | + | 2.64575i | 0.278019 | + | 0.183892i | ||||
\(208\) | 5.65685i | 0.392232i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 14.0000 | 0.966092 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | − | 10.5830i | − | 0.726844i | ||||||
\(213\) | 11.3137i | 0.775203i | ||||||||
\(214\) | − | 5.29150i | − | 0.361720i | ||||||
\(215\) | − | 19.7990i | − | 1.35028i | ||||||
\(216\) | 5.65685i | 0.384900i | ||||||||
\(217\) | −3.74166 | −0.254000 | ||||||||
\(218\) | 10.5830i | 0.716772i | ||||||||
\(219\) | −16.0000 | −1.08118 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.1660i | 1.42378i | ||||||||
\(222\) | −14.9666 | −1.00449 | ||||||||
\(223\) | 9.89949i | 0.662919i | 0.943469 | + | 0.331460i | \(0.107541\pi\) | ||||
−0.943469 | + | 0.331460i | \(0.892459\pi\) | |||||||
\(224\) | − | 2.64575i | − | 0.176777i | ||||||
\(225\) | 9.00000 | 0.600000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.9666 | 0.993370 | 0.496685 | − | 0.867931i | \(-0.334550\pi\) | ||||
0.496685 | + | 0.867931i | \(0.334550\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7083 | 1.23628 | 0.618139 | − | 0.786069i | \(-0.287887\pi\) | ||||
0.618139 | + | 0.786069i | \(0.287887\pi\) | |||||||
\(230\) | 14.9666 | + | 9.89949i | 0.986870 | + | 0.652753i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00000 | 0.525226 | ||||||||
\(233\) | −4.00000 | −0.262049 | −0.131024 | − | 0.991379i | \(-0.541827\pi\) | ||||
−0.131024 | + | 0.991379i | \(0.541827\pi\) | |||||||
\(234\) | − | 5.65685i | − | 0.369800i | ||||||
\(235\) | − | 26.4575i | − | 1.72590i | ||||||
\(236\) | 9.89949i | 0.644402i | ||||||||
\(237\) | −14.9666 | −0.972187 | ||||||||
\(238\) | − | 9.89949i | − | 0.641689i | ||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 5.29150i | 0.341565i | ||||||||
\(241\) | 18.7083 | 1.20511 | 0.602553 | − | 0.798079i | \(-0.294150\pi\) | ||||
0.602553 | + | 0.798079i | \(0.294150\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | − | 9.89949i | − | 0.635053i | ||||||
\(244\) | −3.74166 | −0.239535 | ||||||||
\(245\) | 26.1916 | 1.67332 | ||||||||
\(246\) | −8.00000 | −0.510061 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 1.41421i | − | 0.0898027i | ||||||
\(249\) | − | 21.1660i | − | 1.34134i | ||||||
\(250\) | 14.9666 | 0.946573 | ||||||||
\(251\) | 14.9666 | 0.944685 | 0.472343 | − | 0.881415i | \(-0.343408\pi\) | ||||
0.472343 | + | 0.881415i | \(0.343408\pi\) | |||||||
\(252\) | 2.64575i | 0.166667i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 19.7990i | 1.23986i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.9706i | 1.05859i | 0.848436 | + | 0.529297i | \(0.177544\pi\) | ||||
−0.848436 | + | 0.529297i | \(0.822456\pi\) | |||||||
\(258\) | −7.48331 | −0.465891 | ||||||||
\(259\) | −28.0000 | −1.73984 | ||||||||
\(260\) | − | 21.1660i | − | 1.31266i | ||||||
\(261\) | −8.00000 | −0.495188 | ||||||||
\(262\) | − | 12.7279i | − | 0.786334i | ||||||
\(263\) | 10.5830i | 0.652576i | 0.945270 | + | 0.326288i | \(0.105798\pi\) | ||||
−0.945270 | + | 0.326288i | \(0.894202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.5980i | 2.43248i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.8745i | 0.971504i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 11.3137i | − | 0.689809i | −0.938638 | − | 0.344904i | \(-0.887911\pi\) | ||
0.938638 | − | 0.344904i | \(-0.112089\pi\) | |||||||
\(270\) | − | 21.1660i | − | 1.28812i | ||||||
\(271\) | − | 29.6985i | − | 1.80405i | −0.431679 | − | 0.902027i | \(-0.642079\pi\) | ||
0.431679 | − | 0.902027i | \(-0.357921\pi\) | |||||||
\(272\) | 3.74166 | 0.226871 | ||||||||
\(273\) | 21.1660i | 1.28103i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.74166 | − | 5.65685i | 0.225221 | − | 0.340503i | ||||
\(277\) | 16.0000 | 0.961347 | 0.480673 | − | 0.876900i | \(-0.340392\pi\) | ||||
0.480673 | + | 0.876900i | \(0.340392\pi\) | |||||||
\(278\) | − | 4.24264i | − | 0.254457i | ||||||
\(279\) | 1.41421i | 0.0846668i | ||||||||
\(280\) | 9.89949i | 0.591608i | ||||||||
\(281\) | − | 21.1660i | − | 1.26266i | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||
0.775515 | − | 0.631329i | \(-0.217490\pi\) | |||||||
\(282\) | −10.0000 | −0.595491 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.9666 | −0.883452 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | −29.9333 | −1.75774 | ||||||||
\(291\) | 5.29150i | 0.310193i | ||||||||
\(292\) | − | 11.3137i | − | 0.662085i | ||||||
\(293\) | −18.7083 | −1.09295 | −0.546475 | − | 0.837475i | \(-0.684031\pi\) | ||||
−0.546475 | + | 0.837475i | \(0.684031\pi\) | |||||||
\(294\) | − | 9.89949i | − | 0.577350i | ||||||
\(295\) | − | 37.0405i | − | 2.15658i | ||||||
\(296\) | − | 10.5830i | − | 0.615125i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.5830i | 0.613057i | ||||||||
\(299\) | −14.9666 | + | 22.6274i | −0.865543 | + | 1.30858i | ||||
\(300\) | − | 12.7279i | − | 0.734847i | ||||||
\(301\) | −14.0000 | −0.806947 | ||||||||
\(302\) | −16.0000 | −0.920697 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.0000 | 0.801638 | ||||||||
\(306\) | −3.74166 | −0.213896 | ||||||||
\(307\) | − | 9.89949i | − | 0.564994i | −0.959268 | − | 0.282497i | \(-0.908837\pi\) | ||
0.959268 | − | 0.282497i | \(-0.0911627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 21.1660i | − | 1.20409i | ||||||
\(310\) | 5.29150i | 0.300537i | ||||||||
\(311\) | − | 18.3848i | − | 1.04251i | −0.853402 | − | 0.521253i | \(-0.825465\pi\) | ||
0.853402 | − | 0.521253i | \(-0.174535\pi\) | |||||||
\(312\) | −8.00000 | −0.452911 | ||||||||
\(313\) | −26.1916 | −1.48044 | −0.740218 | − | 0.672366i | \(-0.765278\pi\) | ||||
−0.740218 | + | 0.672366i | \(0.765278\pi\) | |||||||
\(314\) | 11.2250 | 0.633462 | ||||||||
\(315\) | − | 9.89949i | − | 0.557773i | ||||||
\(316\) | − | 10.5830i | − | 0.595341i | ||||||
\(317\) | −8.00000 | −0.449325 | −0.224662 | − | 0.974437i | \(-0.572128\pi\) | ||||
−0.224662 | + | 0.974437i | \(0.572128\pi\) | |||||||
\(318\) | 14.9666 | 0.839287 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.74166 | −0.209165 | ||||||||
\(321\) | 7.48331 | 0.417678 | ||||||||
\(322\) | 7.00000 | − | 10.5830i | 0.390095 | − | 0.589768i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 50.9117i | 2.82407i | ||||||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | −14.9666 | −0.827657 | ||||||||
\(328\) | − | 5.65685i | − | 0.312348i | ||||||
\(329\) | −18.7083 | −1.03142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 14.9666 | 0.821401 | ||||||||
\(333\) | 10.5830i | 0.579945i | ||||||||
\(334\) | 9.89949i | 0.541676i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.74166 | 0.204124 | ||||||||
\(337\) | 21.1660i | 1.15299i | 0.817102 | + | 0.576493i | \(0.195579\pi\) | ||||
−0.817102 | + | 0.576493i | \(0.804421\pi\) | |||||||
\(338\) | 19.0000 | 1.03346 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.0000 | −0.759257 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5203i | − | 1.00000i | ||||||
\(344\) | − | 5.29150i | − | 0.285299i | ||||||
\(345\) | −14.0000 | + | 21.1660i | −0.753735 | + | 1.13954i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.00000 | −0.214731 | −0.107366 | − | 0.994220i | \(-0.534242\pi\) | ||||
−0.107366 | + | 0.994220i | \(0.534242\pi\) | |||||||
\(348\) | 11.3137i | 0.606478i | ||||||||
\(349\) | − | 33.9411i | − | 1.81683i | −0.418073 | − | 0.908413i | \(-0.637294\pi\) | ||
0.418073 | − | 0.908413i | \(-0.362706\pi\) | |||||||
\(350\) | − | 23.8118i | − | 1.27279i | ||||||
\(351\) | 32.0000 | 1.70803 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.3137i | 0.602168i | 0.953598 | + | 0.301084i | \(0.0973484\pi\) | ||||
−0.953598 | + | 0.301084i | \(0.902652\pi\) | |||||||
\(354\) | −14.0000 | −0.744092 | ||||||||
\(355\) | 29.9333 | 1.58869 | ||||||||
\(356\) | −11.2250 | −0.594922 | ||||||||
\(357\) | 14.0000 | 0.740959 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | 10.5830i | 0.558550i | 0.960211 | + | 0.279275i | \(0.0900940\pi\) | ||||
−0.960211 | + | 0.279275i | \(0.909906\pi\) | |||||||
\(360\) | 3.74166 | 0.197203 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 11.2250 | 0.589971 | ||||||||
\(363\) | − | 15.5563i | − | 0.816497i | ||||||
\(364\) | −14.9666 | −0.784465 | ||||||||
\(365\) | 42.3320i | 2.21576i | ||||||||
\(366\) | − | 5.29150i | − | 0.276591i | ||||||
\(367\) | 14.9666 | 0.781252 | 0.390626 | − | 0.920550i | \(-0.372259\pi\) | ||||
0.390626 | + | 0.920550i | \(0.372259\pi\) | |||||||
\(368\) | 4.00000 | + | 2.64575i | 0.208514 | + | 0.137919i | ||||
\(369\) | 5.65685i | 0.294484i | ||||||||
\(370\) | 39.5980i | 2.05860i | ||||||||
\(371\) | 28.0000 | 1.45369 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 10.5830i | 0.547967i | 0.961734 | + | 0.273984i | \(0.0883414\pi\) | ||||
−0.961734 | + | 0.273984i | \(0.911659\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.1660i | 1.09301i | ||||||||
\(376\) | − | 7.07107i | − | 0.364662i | ||||||
\(377\) | − | 45.2548i | − | 2.33074i | ||||||
\(378\) | −14.9666 | −0.769800 | ||||||||
\(379\) | − | 21.1660i | − | 1.08722i | −0.839336 | − | 0.543612i | \(-0.817056\pi\) | ||
0.839336 | − | 0.543612i | \(-0.182944\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 11.3137i | − | 0.579619i | ||||||
\(382\) | − | 15.8745i | − | 0.812210i | ||||||
\(383\) | −29.9333 | −1.52952 | −0.764759 | − | 0.644316i | \(-0.777142\pi\) | ||||
−0.764759 | + | 0.644316i | \(0.777142\pi\) | |||||||
\(384\) | 1.41421i | 0.0721688i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 5.29150i | 0.268982i | ||||||||
\(388\) | −3.74166 | −0.189954 | ||||||||
\(389\) | − | 31.7490i | − | 1.60974i | −0.593452 | − | 0.804869i | \(-0.702235\pi\) | ||
0.593452 | − | 0.804869i | \(-0.297765\pi\) | |||||||
\(390\) | 29.9333 | 1.51573 | ||||||||
\(391\) | 14.9666 | + | 9.89949i | 0.756895 | + | 0.500639i | ||||
\(392\) | 7.00000 | 0.353553 | ||||||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 39.5980i | 1.99239i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.9706i | 0.851728i | 0.904787 | + | 0.425864i | \(0.140030\pi\) | ||||
−0.904787 | + | 0.425864i | \(0.859970\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.00000 | 0.450000 | ||||||||
\(401\) | 21.1660i | 1.05698i | 0.848939 | + | 0.528490i | \(0.177242\pi\) | ||||
−0.848939 | + | 0.528490i | \(0.822758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | −0.398508 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.7083 | 0.929622 | ||||||||
\(406\) | 21.1660i | 1.05045i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.29150i | 0.261968i | ||||||||
\(409\) | − | 11.3137i | − | 0.559427i | −0.960084 | − | 0.279713i | \(-0.909761\pi\) | ||
0.960084 | − | 0.279713i | \(-0.0902395\pi\) | |||||||
\(410\) | 21.1660i | 1.04531i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.9666 | 0.737353 | ||||||||
\(413\) | −26.1916 | −1.28880 | ||||||||
\(414\) | −4.00000 | − | 2.64575i | −0.196589 | − | 0.130032i | ||||
\(415\) | −56.0000 | −2.74893 | ||||||||
\(416\) | − | 5.65685i | − | 0.277350i | ||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.9333 | 1.46234 | 0.731168 | − | 0.682198i | \(-0.238976\pi\) | ||||
0.731168 | + | 0.682198i | \(0.238976\pi\) | |||||||
\(420\) | −14.0000 | −0.683130 | ||||||||
\(421\) | 31.7490i | 1.54735i | 0.633581 | + | 0.773676i | \(0.281584\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | −12.0000 | −0.584151 | ||||||||
\(423\) | 7.07107i | 0.343807i | ||||||||
\(424\) | 10.5830i | 0.513956i | ||||||||
\(425\) | 33.6749 | 1.63347 | ||||||||
\(426\) | − | 11.3137i | − | 0.548151i | ||||||
\(427\) | − | 9.89949i | − | 0.479070i | ||||||
\(428\) | 5.29150i | 0.255774i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.7990i | 0.954792i | ||||||||
\(431\) | 26.4575i | 1.27441i | 0.770693 | + | 0.637207i | \(0.219910\pi\) | ||||
−0.770693 | + | 0.637207i | \(0.780090\pi\) | |||||||
\(432\) | − | 5.65685i | − | 0.272166i | ||||||
\(433\) | 11.2250 | 0.539438 | 0.269719 | − | 0.962939i | \(-0.413069\pi\) | ||||
0.269719 | + | 0.962939i | \(0.413069\pi\) | |||||||
\(434\) | 3.74166 | 0.179605 | ||||||||
\(435\) | − | 42.3320i | − | 2.02967i | ||||||
\(436\) | − | 10.5830i | − | 0.506834i | ||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 16.0000 | 0.764510 | ||||||||
\(439\) | − | 12.7279i | − | 0.607471i | −0.952756 | − | 0.303735i | \(-0.901766\pi\) | ||
0.952756 | − | 0.303735i | \(-0.0982338\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | − | 21.1660i | − | 1.00676i | ||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 14.9666 | 0.710285 | ||||||||
\(445\) | 42.0000 | 1.99099 | ||||||||
\(446\) | − | 9.89949i | − | 0.468755i | ||||||
\(447\) | −14.9666 | −0.707897 | ||||||||
\(448\) | 2.64575i | 0.125000i | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | −9.00000 | −0.424264 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 22.6274i | − | 1.06313i | ||||||
\(454\) | −14.9666 | −0.702419 | ||||||||
\(455\) | 56.0000 | 2.62532 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | −18.7083 | −0.874181 | ||||||||
\(459\) | − | 21.1660i | − | 0.987945i | ||||||
\(460\) | −14.9666 | − | 9.89949i | −0.697823 | − | 0.461566i | ||||
\(461\) | − | 5.65685i | − | 0.263466i | −0.991285 | − | 0.131733i | \(-0.957946\pi\) | ||
0.991285 | − | 0.131733i | \(-0.0420541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | −8.00000 | −0.371391 | ||||||||
\(465\) | −7.48331 | −0.347030 | ||||||||
\(466\) | 4.00000 | 0.185296 | ||||||||
\(467\) | 29.9333 | 1.38515 | 0.692573 | − | 0.721348i | \(-0.256477\pi\) | ||||
0.692573 | + | 0.721348i | \(0.256477\pi\) | |||||||
\(468\) | 5.65685i | 0.261488i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 26.4575i | 1.22039i | ||||||||
\(471\) | 15.8745i | 0.731459i | ||||||||
\(472\) | − | 9.89949i | − | 0.455661i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 14.9666 | 0.687440 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.89949i | 0.453743i | ||||||||
\(477\) | − | 10.5830i | − | 0.484563i | ||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | −29.9333 | −1.36769 | −0.683843 | − | 0.729629i | \(-0.739693\pi\) | ||||
−0.683843 | + | 0.729629i | \(0.739693\pi\) | |||||||
\(480\) | − | 5.29150i | − | 0.241523i | ||||||
\(481\) | −59.8665 | −2.72968 | ||||||||
\(482\) | −18.7083 | −0.852139 | ||||||||
\(483\) | 14.9666 | + | 9.89949i | 0.681005 | + | 0.450443i | ||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 14.0000 | 0.635707 | ||||||||
\(486\) | 9.89949i | 0.449050i | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 3.74166 | 0.169377 | ||||||||
\(489\) | 5.65685i | 0.255812i | ||||||||
\(490\) | −26.1916 | −1.18322 | ||||||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | 8.00000 | 0.360668 | ||||||||
\(493\) | −29.9333 | −1.34813 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.41421i | 0.0635001i | ||||||||
\(497\) | − | 21.1660i | − | 0.949425i | ||||||
\(498\) | 21.1660i | 0.948472i | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | −14.9666 | −0.669328 | ||||||||
\(501\) | −14.0000 | −0.625474 | ||||||||
\(502\) | −14.9666 | −0.667993 | ||||||||
\(503\) | 29.9333 | 1.33466 | 0.667329 | − | 0.744763i | \(-0.267437\pi\) | ||||
0.667329 | + | 0.744763i | \(0.267437\pi\) | |||||||
\(504\) | − | 2.64575i | − | 0.117851i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.8701i | 1.19334i | ||||||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | − | 22.6274i | − | 1.00294i | −0.865174 | − | 0.501471i | \(-0.832792\pi\) | ||
0.865174 | − | 0.501471i | \(-0.167208\pi\) | |||||||
\(510\) | − | 19.7990i | − | 0.876714i | ||||||
\(511\) | 29.9333 | 1.32417 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 16.9706i | − | 0.748539i | ||||||
\(515\) | −56.0000 | −2.46765 | ||||||||
\(516\) | 7.48331 | 0.329435 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 28.0000 | 1.23025 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.1660i | 0.928191i | ||||||||
\(521\) | −3.74166 | −0.163925 | −0.0819625 | − | 0.996635i | \(-0.526119\pi\) | ||||
−0.0819625 | + | 0.996635i | \(0.526119\pi\) | |||||||
\(522\) | 8.00000 | 0.350150 | ||||||||
\(523\) | −14.9666 | −0.654445 | −0.327223 | − | 0.944947i | \(-0.606113\pi\) | ||||
−0.327223 | + | 0.944947i | \(0.606113\pi\) | |||||||
\(524\) | 12.7279i | 0.556022i | ||||||||
\(525\) | 33.6749 | 1.46969 | ||||||||
\(526\) | − | 10.5830i | − | 0.461441i | ||||||
\(527\) | 5.29150i | 0.230501i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | + | 21.1660i | 0.391304 | + | 0.920261i | ||||
\(530\) | − | 39.5980i | − | 1.72003i | ||||||
\(531\) | 9.89949i | 0.429601i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.0000 | −1.38607 | ||||||||
\(534\) | − | 15.8745i | − | 0.686957i | ||||||
\(535\) | − | 19.7990i | − | 0.855985i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.9706i | 0.732334i | ||||||||
\(538\) | 11.3137i | 0.487769i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 21.1660i | 0.910840i | ||||||||
\(541\) | 32.0000 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258536\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258536\pi\) | |||||||
\(542\) | 29.6985i | 1.27566i | ||||||||
\(543\) | 15.8745i | 0.681240i | ||||||||
\(544\) | −3.74166 | −0.160422 | ||||||||
\(545\) | 39.5980i | 1.69619i | ||||||||
\(546\) | − | 21.1660i | − | 0.905822i | ||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.74166 | −0.159690 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −3.74166 | + | 5.65685i | −0.159256 | + | 0.240772i | ||||
\(553\) | 28.0000 | 1.19068 | ||||||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | −56.0000 | −2.37707 | ||||||||
\(556\) | 4.24264i | 0.179928i | ||||||||
\(557\) | 31.7490i | 1.34525i | 0.739984 | + | 0.672624i | \(0.234833\pi\) | ||||
−0.739984 | + | 0.672624i | \(0.765167\pi\) | |||||||
\(558\) | − | 1.41421i | − | 0.0598684i | ||||||
\(559\) | −29.9333 | −1.26604 | ||||||||
\(560\) | − | 9.89949i | − | 0.418330i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.1660i | 0.892834i | ||||||||
\(563\) | 44.8999 | 1.89230 | 0.946152 | − | 0.323722i | \(-0.104934\pi\) | ||||
0.946152 | + | 0.323722i | \(0.104934\pi\) | |||||||
\(564\) | 10.0000 | 0.421076 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 13.2288i | − | 0.555556i | ||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 37.0405i | − | 1.55010i | −0.631901 | − | 0.775049i | \(-0.717725\pi\) | ||
0.631901 | − | 0.775049i | \(-0.282275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.4499 | 0.937860 | ||||||||
\(574\) | 14.9666 | 0.624695 | ||||||||
\(575\) | 36.0000 | + | 23.8118i | 1.50130 | + | 0.993019i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 28.2843i | − | 1.17749i | −0.808319 | − | 0.588745i | \(-0.799622\pi\) | ||
0.808319 | − | 0.588745i | \(-0.200378\pi\) | |||||||
\(578\) | 3.00000 | 0.124784 | ||||||||
\(579\) | 2.82843i | 0.117545i | ||||||||
\(580\) | 29.9333 | 1.24291 | ||||||||
\(581\) | 39.5980i | 1.64280i | ||||||||
\(582\) | − | 5.29150i | − | 0.219340i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.3137i | 0.468165i | ||||||||
\(585\) | − | 21.1660i | − | 0.875107i | ||||||
\(586\) | 18.7083 | 0.772832 | ||||||||
\(587\) | 15.5563i | 0.642079i | 0.947066 | + | 0.321040i | \(0.104032\pi\) | ||||
−0.947066 | + | 0.321040i | \(0.895968\pi\) | |||||||
\(588\) | 9.89949i | 0.408248i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 37.0405i | 1.52493i | ||||||||
\(591\) | − | 8.48528i | − | 0.349038i | ||||||
\(592\) | 10.5830i | 0.434959i | ||||||||
\(593\) | 39.5980i | 1.62609i | 0.582198 | + | 0.813047i | \(0.302193\pi\) | ||||
−0.582198 | + | 0.813047i | \(0.697807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 37.0405i | − | 1.51851i | ||||||
\(596\) | − | 10.5830i | − | 0.433497i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.9666 | − | 22.6274i | 0.612031 | − | 0.925304i | ||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 12.7279i | 0.519615i | ||||||||
\(601\) | − | 45.2548i | − | 1.84598i | −0.384820 | − | 0.922992i | \(-0.625737\pi\) | ||
0.384820 | − | 0.922992i | \(-0.374263\pi\) | |||||||
\(602\) | 14.0000 | 0.570597 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.0000 | 0.651031 | ||||||||
\(605\) | −41.1582 | −1.67332 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.6985i | 1.20542i | 0.797959 | + | 0.602712i | \(0.205913\pi\) | ||||
−0.797959 | + | 0.602712i | \(0.794087\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.9333 | −1.21296 | ||||||||
\(610\) | −14.0000 | −0.566843 | ||||||||
\(611\) | −40.0000 | −1.61823 | ||||||||
\(612\) | 3.74166 | 0.151248 | ||||||||
\(613\) | − | 10.5830i | − | 0.427444i | −0.976895 | − | 0.213722i | \(-0.931441\pi\) | ||
0.976895 | − | 0.213722i | \(-0.0685586\pi\) | |||||||
\(614\) | 9.89949i | 0.399511i | ||||||||
\(615\) | −29.9333 | −1.20703 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 21.1660i | 0.851422i | ||||||||
\(619\) | 14.9666 | 0.601560 | 0.300780 | − | 0.953694i | \(-0.402753\pi\) | ||||
0.300780 | + | 0.953694i | \(0.402753\pi\) | |||||||
\(620\) | − | 5.29150i | − | 0.212512i | ||||||
\(621\) | 14.9666 | − | 22.6274i | 0.600590 | − | 0.908007i | ||||
\(622\) | 18.3848i | 0.737162i | ||||||||
\(623\) | − | 29.6985i | − | 1.18984i | ||||||
\(624\) | 8.00000 | 0.320256 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 26.1916 | 1.04683 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.2250 | −0.447925 | ||||||||
\(629\) | 39.5980i | 1.57887i | ||||||||
\(630\) | 9.89949i | 0.394405i | ||||||||
\(631\) | 10.5830i | 0.421303i | 0.977561 | + | 0.210651i | \(0.0675585\pi\) | ||||
−0.977561 | + | 0.210651i | \(0.932442\pi\) | |||||||
\(632\) | 10.5830i | 0.420969i | ||||||||
\(633\) | − | 16.9706i | − | 0.674519i | ||||||
\(634\) | 8.00000 | 0.317721 | ||||||||
\(635\) | −29.9333 | −1.18787 | ||||||||
\(636\) | −14.9666 | −0.593465 | ||||||||
\(637\) | − | 39.5980i | − | 1.56893i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | −0.316475 | ||||||||
\(640\) | 3.74166 | 0.147902 | ||||||||
\(641\) | 42.3320i | 1.67201i | 0.548719 | + | 0.836007i | \(0.315116\pi\) | ||||
−0.548719 | + | 0.836007i | \(0.684884\pi\) | |||||||
\(642\) | −7.48331 | −0.295343 | ||||||||
\(643\) | −44.8999 | −1.77068 | −0.885339 | − | 0.464945i | \(-0.846074\pi\) | ||||
−0.885339 | + | 0.464945i | \(0.846074\pi\) | |||||||
\(644\) | −7.00000 | + | 10.5830i | −0.275839 | + | 0.417029i | ||||
\(645\) | −28.0000 | −1.10250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 38.1838i | − | 1.50116i | −0.660780 | − | 0.750579i | \(-0.729774\pi\) | ||
0.660780 | − | 0.750579i | \(-0.270226\pi\) | |||||||
\(648\) | 5.00000 | 0.196419 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 50.9117i | − | 1.99692i | ||||||
\(651\) | 5.29150i | 0.207390i | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 46.0000 | 1.80012 | 0.900060 | − | 0.435767i | \(-0.143523\pi\) | ||||
0.900060 | + | 0.435767i | \(0.143523\pi\) | |||||||
\(654\) | 14.9666 | 0.585242 | ||||||||
\(655\) | − | 47.6235i | − | 1.86081i | ||||||
\(656\) | 5.65685i | 0.220863i | ||||||||
\(657\) | − | 11.3137i | − | 0.441390i | ||||||
\(658\) | 18.7083 | 0.729325 | ||||||||
\(659\) | − | 26.4575i | − | 1.03064i | −0.856998 | − | 0.515319i | \(-0.827673\pi\) | ||
0.856998 | − | 0.515319i | \(-0.172327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.2250 | 0.436601 | 0.218300 | − | 0.975882i | \(-0.429949\pi\) | ||||
0.218300 | + | 0.975882i | \(0.429949\pi\) | |||||||
\(662\) | −4.00000 | −0.155464 | ||||||||
\(663\) | 29.9333 | 1.16251 | ||||||||
\(664\) | −14.9666 | −0.580818 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 10.5830i | − | 0.410083i | ||||||
\(667\) | −32.0000 | − | 21.1660i | −1.23904 | − | 0.819551i | ||||
\(668\) | − | 9.89949i | − | 0.383023i | ||||||
\(669\) | 14.0000 | 0.541271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.74166 | −0.144338 | ||||||||
\(673\) | −36.0000 | −1.38770 | −0.693849 | − | 0.720121i | \(-0.744086\pi\) | ||||
−0.693849 | + | 0.720121i | \(0.744086\pi\) | |||||||
\(674\) | − | 21.1660i | − | 0.815284i | ||||||
\(675\) | − | 50.9117i | − | 1.95959i | ||||||
\(676\) | −19.0000 | −0.730769 | ||||||||
\(677\) | 11.2250 | 0.431411 | 0.215705 | − | 0.976458i | \(-0.430795\pi\) | ||||
0.215705 | + | 0.976458i | \(0.430795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 9.89949i | − | 0.379908i | ||||||
\(680\) | 14.0000 | 0.536875 | ||||||||
\(681\) | − | 21.1660i | − | 0.811083i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.5203i | 0.707107i | ||||||||
\(687\) | − | 26.4575i | − | 1.00942i | ||||||
\(688\) | 5.29150i | 0.201737i | ||||||||
\(689\) | 59.8665 | 2.28073 | ||||||||
\(690\) | 14.0000 | − | 21.1660i | 0.532971 | − | 0.805776i | ||||
\(691\) | 29.6985i | 1.12978i | 0.825165 | + | 0.564892i | \(0.191082\pi\) | ||||
−0.825165 | + | 0.564892i | \(0.808918\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | − | 15.8745i | − | 0.602154i | ||||||
\(696\) | − | 11.3137i | − | 0.428845i | ||||||
\(697\) | 21.1660i | 0.801720i | ||||||||
\(698\) | 33.9411i | 1.28469i | ||||||||
\(699\) | 5.65685i | 0.213962i | ||||||||
\(700\) | 23.8118i | 0.900000i | ||||||||
\(701\) | − | 10.5830i | − | 0.399715i | −0.979825 | − | 0.199857i | \(-0.935952\pi\) | ||
0.979825 | − | 0.199857i | \(-0.0640479\pi\) | |||||||
\(702\) | −32.0000 | −1.20776 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −37.4166 | −1.40919 | ||||||||
\(706\) | − | 11.3137i | − | 0.425797i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 14.0000 | 0.526152 | ||||||||
\(709\) | − | 10.5830i | − | 0.397453i | −0.980055 | − | 0.198727i | \(-0.936319\pi\) | ||
0.980055 | − | 0.198727i | \(-0.0636806\pi\) | |||||||
\(710\) | −29.9333 | −1.12338 | ||||||||
\(711\) | − | 10.5830i | − | 0.396894i | ||||||
\(712\) | 11.2250 | 0.420674 | ||||||||
\(713\) | −3.74166 | + | 5.65685i | −0.140126 | + | 0.211851i | ||||
\(714\) | −14.0000 | −0.523937 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | − | 11.3137i | − | 0.422518i | ||||||
\(718\) | − | 10.5830i | − | 0.394954i | ||||||
\(719\) | − | 9.89949i | − | 0.369189i | −0.982815 | − | 0.184594i | \(-0.940903\pi\) | ||
0.982815 | − | 0.184594i | \(-0.0590972\pi\) | |||||||
\(720\) | −3.74166 | −0.139443 | ||||||||
\(721\) | 39.5980i | 1.47471i | ||||||||
\(722\) | 19.0000 | 0.707107 | ||||||||
\(723\) | − | 26.4575i | − | 0.983965i | ||||||
\(724\) | −11.2250 | −0.417173 | ||||||||
\(725\) | −72.0000 | −2.67401 | ||||||||
\(726\) | 15.5563i | 0.577350i | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 14.9666 | 0.554700 | ||||||||
\(729\) | −29.0000 | −1.07407 | ||||||||
\(730\) | − | 42.3320i | − | 1.56678i | ||||||
\(731\) | 19.7990i | 0.732292i | ||||||||
\(732\) | 5.29150i | 0.195580i | ||||||||
\(733\) | 26.1916 | 0.967409 | 0.483704 | − | 0.875231i | \(-0.339291\pi\) | ||||
0.483704 | + | 0.875231i | \(0.339291\pi\) | |||||||
\(734\) | −14.9666 | −0.552428 | ||||||||
\(735\) | − | 37.0405i | − | 1.36626i | ||||||
\(736\) | −4.00000 | − | 2.64575i | −0.147442 | − | 0.0975237i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 5.65685i | − | 0.208232i | ||||||
\(739\) | 12.0000 | 0.441427 | 0.220714 | − | 0.975339i | \(-0.429161\pi\) | ||||
0.220714 | + | 0.975339i | \(0.429161\pi\) | |||||||
\(740\) | − | 39.5980i | − | 1.45565i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.0000 | −1.02791 | ||||||||
\(743\) | 31.7490i | 1.16476i | 0.812917 | + | 0.582379i | \(0.197878\pi\) | ||||
−0.812917 | + | 0.582379i | \(0.802122\pi\) | |||||||
\(744\) | −2.00000 | −0.0733236 | ||||||||
\(745\) | 39.5980i | 1.45076i | ||||||||
\(746\) | − | 10.5830i | − | 0.387471i | ||||||
\(747\) | 14.9666 | 0.547600 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.0000 | −0.511549 | ||||||||
\(750\) | − | 21.1660i | − | 0.772873i | ||||||
\(751\) | 31.7490i | 1.15854i | 0.815136 | + | 0.579269i | \(0.196662\pi\) | ||||
−0.815136 | + | 0.579269i | \(0.803338\pi\) | |||||||
\(752\) | 7.07107i | 0.257855i | ||||||||
\(753\) | − | 21.1660i | − | 0.771332i | ||||||
\(754\) | 45.2548i | 1.64808i | ||||||||
\(755\) | −59.8665 | −2.17877 | ||||||||
\(756\) | 14.9666 | 0.544331 | ||||||||
\(757\) | − | 10.5830i | − | 0.384646i | −0.981332 | − | 0.192323i | \(-0.938398\pi\) | ||
0.981332 | − | 0.192323i | \(-0.0616021\pi\) | |||||||
\(758\) | 21.1660i | 0.768784i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 22.6274i | − | 0.820243i | −0.912031 | − | 0.410122i | \(-0.865486\pi\) | ||
0.912031 | − | 0.410122i | \(-0.134514\pi\) | |||||||
\(762\) | 11.3137i | 0.409852i | ||||||||
\(763\) | 28.0000 | 1.01367 | ||||||||
\(764\) | 15.8745i | 0.574320i | ||||||||
\(765\) | −14.0000 | −0.506171 | ||||||||
\(766\) | 29.9333 | 1.08153 | ||||||||
\(767\) | −56.0000 | −2.02204 | ||||||||
\(768\) | − | 1.41421i | − | 0.0510310i | ||||||
\(769\) | 33.6749 | 1.21435 | 0.607174 | − | 0.794569i | \(-0.292303\pi\) | ||||
0.607174 | + | 0.794569i | \(0.292303\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0000 | 0.864339 | ||||||||
\(772\) | −2.00000 | −0.0719816 | ||||||||
\(773\) | 3.74166 | 0.134578 | 0.0672890 | − | 0.997734i | \(-0.478565\pi\) | ||||
0.0672890 | + | 0.997734i | \(0.478565\pi\) | |||||||
\(774\) | − | 5.29150i | − | 0.190199i | ||||||
\(775\) | 12.7279i | 0.457200i | ||||||||
\(776\) | 3.74166 | 0.134318 | ||||||||
\(777\) | 39.5980i | 1.42057i | ||||||||
\(778\) | 31.7490i | 1.13826i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −29.9333 | −1.07178 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −14.9666 | − | 9.89949i | −0.535206 | − | 0.354005i | ||||
\(783\) | 45.2548i | 1.61728i | ||||||||
\(784\) | −7.00000 | −0.250000 | ||||||||
\(785\) | 42.0000 | 1.49904 | ||||||||
\(786\) | −18.0000 | −0.642039 | ||||||||
\(787\) | −29.9333 | −1.06701 | −0.533503 | − | 0.845798i | \(-0.679125\pi\) | ||||
−0.533503 | + | 0.845798i | \(0.679125\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 14.9666 | 0.532826 | ||||||||
\(790\) | − | 39.5980i | − | 1.40883i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 21.1660i | − | 0.751627i | ||||||
\(794\) | − | 16.9706i | − | 0.602263i | ||||||
\(795\) | 56.0000 | 1.98612 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.6749 | 1.19283 | 0.596413 | − | 0.802677i | \(-0.296592\pi\) | ||||
0.596413 | + | 0.802677i | \(0.296592\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.4575i | 0.936000i | ||||||||
\(800\) | −9.00000 | −0.318198 | ||||||||
\(801\) | −11.2250 | −0.396615 | ||||||||
\(802\) | − | 21.1660i | − | 0.747398i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.1916 | − | 39.5980i | 0.923133 | − | 1.39565i | ||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | −16.0000 | −0.563227 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.0000 | −0.351581 | −0.175791 | − | 0.984428i | \(-0.556248\pi\) | ||||
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | −18.7083 | −0.657342 | ||||||||
\(811\) | − | 4.24264i | − | 0.148979i | −0.997222 | − | 0.0744896i | \(-0.976267\pi\) | ||
0.997222 | − | 0.0744896i | \(-0.0237328\pi\) | |||||||
\(812\) | − | 21.1660i | − | 0.742781i | ||||||
\(813\) | −42.0000 | −1.47300 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.9666 | 0.524258 | ||||||||
\(816\) | − | 5.29150i | − | 0.185240i | ||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 11.3137i | 0.395575i | ||||||||
\(819\) | −14.9666 | −0.522976 | ||||||||
\(820\) | − | 21.1660i | − | 0.739149i | ||||||
\(821\) | 48.0000 | 1.67521 | 0.837606 | − | 0.546275i | \(-0.183955\pi\) | ||||
0.837606 | + | 0.546275i | \(0.183955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | −14.9666 | −0.521387 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.1916 | 0.911322 | ||||||||
\(827\) | − | 47.6235i | − | 1.65603i | −0.560704 | − | 0.828016i | \(-0.689470\pi\) | ||
0.560704 | − | 0.828016i | \(-0.310530\pi\) | |||||||
\(828\) | 4.00000 | + | 2.64575i | 0.139010 | + | 0.0919462i | ||||
\(829\) | 39.5980i | 1.37529i | 0.726045 | + | 0.687647i | \(0.241356\pi\) | ||||
−0.726045 | + | 0.687647i | \(0.758644\pi\) | |||||||
\(830\) | 56.0000 | 1.94379 | ||||||||
\(831\) | − | 22.6274i | − | 0.784936i | ||||||
\(832\) | 5.65685i | 0.196116i | ||||||||
\(833\) | −26.1916 | −0.907485 | ||||||||
\(834\) | −6.00000 | −0.207763 | ||||||||
\(835\) | 37.0405i | 1.28184i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | −29.9333 | −1.03403 | ||||||||
\(839\) | −14.9666 | −0.516705 | −0.258353 | − | 0.966051i | \(-0.583180\pi\) | ||||
−0.258353 | + | 0.966051i | \(0.583180\pi\) | |||||||
\(840\) | 14.0000 | 0.483046 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | − | 31.7490i | − | 1.09414i | ||||||
\(843\) | −29.9333 | −1.03096 | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 71.0915 | 2.44562 | ||||||||
\(846\) | − | 7.07107i | − | 0.243108i | ||||||
\(847\) | 29.1033i | 1.00000i | ||||||||
\(848\) | − | 10.5830i | − | 0.363422i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −33.6749 | −1.15504 | ||||||||
\(851\) | −28.0000 | + | 42.3320i | −0.959828 | + | 1.45112i | ||||
\(852\) | 11.3137i | 0.387601i | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 9.89949i | 0.338754i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 5.29150i | − | 0.180860i | ||||||
\(857\) | − | 11.3137i | − | 0.386469i | −0.981153 | − | 0.193234i | \(-0.938102\pi\) | ||
0.981153 | − | 0.193234i | \(-0.0618978\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.5269i | 1.10980i | 0.831916 | + | 0.554902i | \(0.187244\pi\) | ||||
−0.831916 | + | 0.554902i | \(0.812756\pi\) | |||||||
\(860\) | − | 19.7990i | − | 0.675140i | ||||||
\(861\) | 21.1660i | 0.721336i | ||||||||
\(862\) | − | 26.4575i | − | 0.901146i | ||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 5.65685i | 0.192450i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.2250 | −0.381440 | ||||||||
\(867\) | 4.24264i | 0.144088i | ||||||||
\(868\) | −3.74166 | −0.127000 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 42.3320i | 1.43519i | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.5830i | 0.358386i | ||||||||
\(873\) | −3.74166 | −0.126636 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 39.5980i | − | 1.33866i | ||||||
\(876\) | −16.0000 | −0.540590 | ||||||||
\(877\) | 8.00000 | 0.270141 | 0.135070 | − | 0.990836i | \(-0.456874\pi\) | ||||
0.135070 | + | 0.990836i | \(0.456874\pi\) | |||||||
\(878\) | 12.7279i | 0.429547i | ||||||||
\(879\) | 26.4575i | 0.892390i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.2250 | −0.378179 | −0.189089 | − | 0.981960i | \(-0.560554\pi\) | ||||
−0.189089 | + | 0.981960i | \(0.560554\pi\) | |||||||
\(882\) | 7.00000 | 0.235702 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 21.1660i | 0.711890i | ||||||||
\(885\) | −52.3832 | −1.76084 | ||||||||
\(886\) | 4.00000 | 0.134383 | ||||||||
\(887\) | − | 7.07107i | − | 0.237423i | −0.992929 | − | 0.118712i | \(-0.962124\pi\) | ||
0.992929 | − | 0.118712i | \(-0.0378764\pi\) | |||||||
\(888\) | −14.9666 | −0.502247 | ||||||||
\(889\) | 21.1660i | 0.709885i | ||||||||
\(890\) | −42.0000 | −1.40784 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.89949i | 0.331460i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 14.9666 | 0.500559 | ||||||||
\(895\) | 44.8999 | 1.50084 | ||||||||
\(896\) | − | 2.64575i | − | 0.0883883i | ||||||
\(897\) | 32.0000 | + | 21.1660i | 1.06845 | + | 0.706713i | ||||
\(898\) | −12.0000 | −0.400445 | ||||||||
\(899\) | − | 11.3137i | − | 0.377333i | ||||||
\(900\) | 9.00000 | 0.300000 | ||||||||
\(901\) | − | 39.5980i | − | 1.31920i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.7990i | 0.658869i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42.0000 | 1.39613 | ||||||||
\(906\) | 22.6274i | 0.751746i | ||||||||
\(907\) | − | 5.29150i | − | 0.175701i | −0.996134 | − | 0.0878507i | \(-0.972000\pi\) | ||
0.996134 | − | 0.0878507i | \(-0.0279999\pi\) | |||||||
\(908\) | 14.9666 | 0.496685 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −56.0000 | −1.85638 | ||||||||
\(911\) | − | 31.7490i | − | 1.05189i | −0.850518 | − | 0.525946i | \(-0.823711\pi\) | ||
0.850518 | − | 0.525946i | \(-0.176289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 19.7990i | − | 0.654534i | ||||||
\(916\) | 18.7083 | 0.618139 | ||||||||
\(917\) | −33.6749 | −1.11204 | ||||||||
\(918\) | 21.1660i | 0.698582i | ||||||||
\(919\) | − | 10.5830i | − | 0.349101i | −0.984648 | − | 0.174551i | \(-0.944153\pi\) | ||
0.984648 | − | 0.174551i | \(-0.0558472\pi\) | |||||||
\(920\) | 14.9666 | + | 9.89949i | 0.493435 | + | 0.326377i | ||||
\(921\) | −14.0000 | −0.461316 | ||||||||
\(922\) | 5.65685i | 0.186299i | ||||||||
\(923\) | − | 45.2548i | − | 1.48958i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 95.2470i | 3.13170i | ||||||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | 14.9666 | 0.491569 | ||||||||
\(928\) | 8.00000 | 0.262613 | ||||||||
\(929\) | − | 56.5685i | − | 1.85595i | −0.372638 | − | 0.927977i | \(-0.621547\pi\) | ||
0.372638 | − | 0.927977i | \(-0.378453\pi\) | |||||||
\(930\) | 7.48331 | 0.245388 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.00000 | −0.131024 | ||||||||
\(933\) | −26.0000 | −0.851202 | ||||||||
\(934\) | −29.9333 | −0.979446 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 5.65685i | − | 0.184900i | ||||||
\(937\) | 48.6415 | 1.58905 | 0.794525 | − | 0.607231i | \(-0.207720\pi\) | ||||
0.794525 | + | 0.607231i | \(0.207720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37.0405i | 1.20877i | ||||||||
\(940\) | − | 26.4575i | − | 0.862949i | ||||||
\(941\) | 3.74166 | 0.121975 | 0.0609873 | − | 0.998139i | \(-0.480575\pi\) | ||||
0.0609873 | + | 0.998139i | \(0.480575\pi\) | |||||||
\(942\) | − | 15.8745i | − | 0.517219i | ||||||
\(943\) | −14.9666 | + | 22.6274i | −0.487381 | + | 0.736850i | ||||
\(944\) | 9.89949i | 0.322201i | ||||||||
\(945\) | −56.0000 | −1.82168 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 60.0000 | 1.94974 | 0.974869 | − | 0.222779i | \(-0.0715128\pi\) | ||||
0.974869 | + | 0.222779i | \(0.0715128\pi\) | |||||||
\(948\) | −14.9666 | −0.486094 | ||||||||
\(949\) | 64.0000 | 2.07753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.3137i | 0.366872i | ||||||||
\(952\) | − | 9.89949i | − | 0.320844i | ||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 10.5830i | 0.342637i | ||||||||
\(955\) | − | 59.3970i | − | 1.92204i | ||||||
\(956\) | 8.00000 | 0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.9333 | 0.967100 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.29150i | 0.170783i | ||||||||
\(961\) | 29.0000 | 0.935484 | ||||||||
\(962\) | 59.8665 | 1.93017 | ||||||||
\(963\) | 5.29150i | 0.170516i | ||||||||
\(964\) | 18.7083 | 0.602553 | ||||||||
\(965\) | 7.48331 | 0.240896 | ||||||||
\(966\) | −14.9666 | − | 9.89949i | −0.481543 | − | 0.318511i | ||||
\(967\) | 48.0000 | 1.54358 | 0.771788 | − | 0.635880i | \(-0.219363\pi\) | ||||
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.0000 | −0.449513 | ||||||||
\(971\) | −14.9666 | −0.480302 | −0.240151 | − | 0.970736i | \(-0.577197\pi\) | ||||
−0.240151 | + | 0.970736i | \(0.577197\pi\) | |||||||
\(972\) | − | 9.89949i | − | 0.317526i | ||||||
\(973\) | −11.2250 | −0.359856 | ||||||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 72.0000 | 2.30585 | ||||||||
\(976\) | −3.74166 | −0.119768 | ||||||||
\(977\) | 21.1660i | 0.677161i | 0.940937 | + | 0.338580i | \(0.109947\pi\) | ||||
−0.940937 | + | 0.338580i | \(0.890053\pi\) | |||||||
\(978\) | − | 5.65685i | − | 0.180886i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 26.1916 | 0.836660 | ||||||||
\(981\) | − | 10.5830i | − | 0.337889i | ||||||
\(982\) | −20.0000 | −0.638226 | ||||||||
\(983\) | −29.9333 | −0.954723 | −0.477361 | − | 0.878707i | \(-0.658407\pi\) | ||||
−0.477361 | + | 0.878707i | \(0.658407\pi\) | |||||||
\(984\) | −8.00000 | −0.255031 | ||||||||
\(985\) | −22.4499 | −0.715315 | ||||||||
\(986\) | 29.9333 | 0.953269 | ||||||||
\(987\) | 26.4575i | 0.842152i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.0000 | + | 21.1660i | −0.445174 | + | 0.673040i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | − | 1.41421i | − | 0.0449013i | ||||||
\(993\) | − | 5.65685i | − | 0.179515i | ||||||
\(994\) | 21.1660i | 0.671345i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 21.1660i | − | 0.670671i | ||||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | −4.00000 | −0.126618 | ||||||||
\(999\) | 59.8665 | 1.89409 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 322.2.c.b.321.1 | ✓ | 4 | |
3.2 | odd | 2 | 2898.2.g.e.2575.4 | 4 | |||
4.3 | odd | 2 | 2576.2.f.c.321.3 | 4 | |||
7.6 | odd | 2 | inner | 322.2.c.b.321.4 | yes | 4 | |
21.20 | even | 2 | 2898.2.g.e.2575.2 | 4 | |||
23.22 | odd | 2 | inner | 322.2.c.b.321.2 | yes | 4 | |
28.27 | even | 2 | 2576.2.f.c.321.2 | 4 | |||
69.68 | even | 2 | 2898.2.g.e.2575.1 | 4 | |||
92.91 | even | 2 | 2576.2.f.c.321.4 | 4 | |||
161.160 | even | 2 | inner | 322.2.c.b.321.3 | yes | 4 | |
483.482 | odd | 2 | 2898.2.g.e.2575.3 | 4 | |||
644.643 | odd | 2 | 2576.2.f.c.321.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.c.b.321.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
322.2.c.b.321.2 | yes | 4 | 23.22 | odd | 2 | inner | |
322.2.c.b.321.3 | yes | 4 | 161.160 | even | 2 | inner | |
322.2.c.b.321.4 | yes | 4 | 7.6 | odd | 2 | inner | |
2576.2.f.c.321.1 | 4 | 644.643 | odd | 2 | |||
2576.2.f.c.321.2 | 4 | 28.27 | even | 2 | |||
2576.2.f.c.321.3 | 4 | 4.3 | odd | 2 | |||
2576.2.f.c.321.4 | 4 | 92.91 | even | 2 | |||
2898.2.g.e.2575.1 | 4 | 69.68 | even | 2 | |||
2898.2.g.e.2575.2 | 4 | 21.20 | even | 2 | |||
2898.2.g.e.2575.3 | 4 | 483.482 | odd | 2 | |||
2898.2.g.e.2575.4 | 4 | 3.2 | odd | 2 |